Rank and crank moments for overpartitions

Details Rank and crank moments for overpartitions Rank and crank moments for overpartitions

2008-07-30

arxiv.org/abs/0807.4877v1

Journal of Number Theory 129 (2009), 1758-1772

Mathematics

Number Theory

14 pages

Scientific paper

We study two types of crank moments and two types of rank moments for overpartitions. We show that the crank moments and their derivatives, along with certain linear combinations of the rank moments and their derivatives, can be written in terms of quasimodular forms. We then use this fact to prove exact relations involving the moments as well as congruence properties modulo 3, 5, and 7 for some combinatorial functions which may be expressed in terms of the second moments. Finally, we establish a congruence modulo 3 involving one such combinatorial function and the Hurwitz class number H(n).

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